Former Republican presidential candidate Newt Gingrich says that House Republicans can't win a fight to cut spending by holding the debt ceiling hostage because President Barack Obama is "going out of his way to bully" them.

"In the end it's a threat they can't sustain," Gingrich told CBS on Tuesday. "No one is going to default, no one is going to allow the United States to not pay its bills, no one is going to accept the economic costs. It rallies the entire business community to the president's side."

The former House Speaker recommended that Republicans instead use the continuing resolution that funds government and the sequester to fight for spending cuts.

"I don't think we should pick fights where we can't, in fact in the end, enforce our will because we have no evidence, in the end, that Barack Obama's going to compromise," he explained. "Nothing he's done in the last couple of months would imply that he's going to compromise."

"So, therefore do you agree that the president is right in not negotiating?" CBS host Charlie Rose wondered.

"No," Gingrich insisted. "I think the president's wrong, but he's a fact [Republicans must deal with]. I think this president is deliberately seeking confrontation, I think he's going out of his way to bully the the House Republicans. And I think the House Republicans ought to pick the continuing resolution and the sequester."

"Look, I wouldn't ask him to offer spending cuts because he's clearly not going to do it. Asking Barack Obama not to be a big-spending, high-taxing liberal is denial of everything we've learned about him in his career."

CBS host Norah O'Donnell also asked Gingrich to respond to criticism the National Rifle Association (NRA) is receiving after they released a first-person shooting game for Apple's iPhone and iPad that is targeted at children as young as four.

"My understanding is that it's a gun-saftey app and it's for young hunters to learn gun safety," the Georgia Republican replied. "I would just recommend people watch the entire app before they render judgement."

"I think it's amazing that we're having all this discussion about gun control, the president's hometown of Chicago is the murder capitol of the United States," he opined. "Over 500 people were killed there last year. Vice President [Joe] Biden doesn't seem to want to go there. I'm trying to get the House Republicans to hold hearings there. It's illegal to have all the guns that are killing people in Chicago. If gun control works Chicago ought to be safe."

Watch this video from CBS' This Morning, broadcast Jan. 15, 2013.